Problem: Simplify the following expression: $q = \dfrac{y^2 - 3y - 70}{y + 7} $
Solution: First factor the polynomial in the numerator. $ y^2 - 3y - 70 = (y + 7)(y - 10) $ So we can rewrite the expression as: $q = \dfrac{(y + 7)(y - 10)}{y + 7} $ We can divide the numerator and denominator by $(y + 7)$ on condition that $y \neq -7$ Therefore $q = y - 10; y \neq -7$